Why is the policy not a part of the MDP definition?
The MDP defines the environment (which corresponds to the task that you need to solve), so it defines e.g. the states of the environment, the actions that you can take in those states, the probabilities of transitioning from one state to the other and the probabilities of getting a reward when you take a certain action in a certain state. 

The policy corresponds to a strategy that the RL agent can follow to act in that environment. Note that the MDP doesn't define what the agent does in each state. That's why you need the policy! An optimal policy for a specific MDP corresponds to the strategy that, if followed, is guaranteed to give you the highest amount of reward in that environment. However, there are multiple strategies, most of them are not optimal. This should clarify why the policy is not part of the definition of the MDP.